In this paper we study from a numerical analysis perspective the fractional step kinetic Monte Carlo (FS-KMC) algorithms proposed in [G. Arampatzis, M. A. Katsoulakis, P. Plechac, M. Taufer, and L. Xu, J. Comput. Phys., 231 (2012), pp. 7795--7814] for the parallel simulation of spatially distributed particle systems on a lattice. FS-KMC are fractional step algorithms with a time-stepping window $\Delta t$, and as such they are inherently partially asynchronous since there is no processor communication during the period $\Delta t$. In this contribution we primarily focus on the error analysis of FS-KMC algorithms as approximations of conventional, serial KMC. A key aspect of the presented analysis relies on emphasizing a goal-oriented approach for suitably defined macroscopic observables (e.g., density, energy, correlations, surface roughness), rather than focusing on strong topology estimates for individual trajectories. The presented error analysis allows us to compare different parallelization strategies and their processor communications by relating the algorithm partial asynchrony to the time step $\Delta t$ and a prescribed error tolerance. Finally, the presented results show that previously developed KMC algorithms based on domain decomposition principles also allow for simulations with controlled errors for macroscopic of observables, while their partial asynchrony also can be demonstrated and quantified.